I see Marsha Blackburn being a real possibility of being appointed, but she's too conservative to keep the seat non-competitive.
Please name one Democrat who would have a non-zero chance of beating Blackburn.
Jim Cooper, Phil Bredesen, and Mike McWherter. Besides them and the fact that none of them would both run AND get national funding, I should clarify I assume you don't literally mean "non-zero".
Bredesen was a very popular Governor when he left office in 2010 but Politics has changed a lot since 2010(political polarization) I think and I started following politics in 2009. I think the 24/7 news cycle is more mainstream than it was in 2010.
Bredesen had a chance to challenge Corker in 2012 but he passed since him and Corker are good friends I think.
Cooper-He had his chance in 1993 vs the late Fred Thompson in a Special Election to replace Al Gore but he didn't win.